Question

Find the greatest number of 3-digit exactly divisible by 8, 10 and 12.​

Answer 1

Answer:

960

Step-by-step explanation:

Let us calculate the L.C.M 8, 10 and 12

L.C.M of 8, 10, 12 = 2 x 2 x 2 x 3 x 5

LCM of 8, 10, 12 = 120

We have to find the greatest 3 digit multiple of 120

∴ the number is

120 x 8 = 960

120 x 10 = 1200

120 x 12 = 1440

The 1200 and 1440 are not 3-digit numbers.

Hence, the greatest 3- digit number exactly divisible by 8, 10 & 12 is 960.

Now, let us check whether 960 is divisible by 8, 10 and 12.

960 ÷ 8 = 120

960 ÷ 10 = 96

960 ÷ 12 = 80

So the greatest 3-digit number is 960.

Answer 2

Step-by-step explanation:

Let us calculate the L.C.M 8, 10 and 12

L.C.M of 8, 10, 12 = 2 x 2 x 2 x 3 x 5

LCM of 8, 10, 12 = 120

We have to find the greatest 3 digit multiple of 120

∴ the number is

120 x 8 = 960

120 x 10 = 1200

120 x 12 = 1440

The 1200 and 1440 are not 3-digit numbers.

Hence, the greatest 3- digit number exactly divisible by 8, 10 & 12 is 960.

Now, let us check whether 960 is divisible by 8, 10 and 12.

960 ÷ 8 = 120

960 ÷ 10 = 96

960 ÷ 12 = 80

So the greatest 3-digit number is 960.